I have a couple physics questions I need help with please! If you could show me step-by-step directions, I'd really appreciate it!
A boat with a horizontal tow rope pulls a water skier. She skis off to the side, so the rope makes an angle of 15.0 degrees with the forward direction of motion. If the tension in the rope is 180 N, how much work does the rope do on the skier during a forward displacement of 300.0 m?
A 715 N person walks up three flights of stairs, covering a total vertical distance of 10.5 m. (a) If, as is typical, only 20% of the caloric (food) energy is converted to work by the muscles, how many joules and food calories of energy did the person use? (One food calorie=4186 J.) (b) What happened to the other 80% of the food energy?
A 0.420 kg soccer ball is initially moving at 2.00 m/s. A soccer player kicks the ball, exerting a constant 40.0 N force in tbe same direction as the ball's motion. Over what distance must her foot be in contact with the ball to increase the ball's speed to 6.00 m/s?
A 1200 kg car is moving on the freeway at 65 mph. (a) Find the magnitude of its momentum and its kinetic energy in SI units. (b) If a 2400 kg SUV has the same as the 1200 kg car, how much momentum and kinetic energy does it have?
The magnitude of the momentum of a cat is p. What would be the magnitude of the momentum (in terms of p) of a dog having three times the mass of the cat if it had (a) the same speed as the cat, and (b) the same kinetic energy as the cat?
On a highly polished, essentially frictionless lunch counter, a 0.500 kg submarine sandwich moving 3.00 m/s to the left collides with an 0.250 kg grilled cheese sandwich moving 1.20 m/s to the right. (a) If the two sandwiches stick together, what is their final velocity? (b) How much mechanical energy dissipates in the collision? Where did this energy go?
A catcher catches a 145 g baseball traveling horizontally at 36.0 m/s. (a) How large an impulse does the ball give to the catcher? (b) If the ball takes 20 ms to stop once it is in contact with the catcher's glove, what average force did the ball exert on the catcher?
A 0.300 kg glider is moving to the right on a frictionless, horizontal air track with a speed of 0.80 m/s when it makes a head-on collision with a stationary 0.150 kg glider. (a) Find the magnitude and direction of the final velocity of each glider if the collision is elastic. (b) Find the final kinectic energy of each glider.
ANSWER 3P
Sure, I'd be happy to help you with these physics questions! Let's go through each question one by one and break down the steps needed to find the answers.
Question 1:
To find the work done by the rope on the skier, we can use the formula:
Work = Force x Distance x cos(theta)
where
Force = 180 N (given tension in the rope)
Distance = 300.0 m (given forward displacement)
theta = 15.0 degrees (angle between the rope and the forward direction)
1. Start by converting the angle from degrees to radians by using the formula:
radians = degrees x (pi/180)
theta_radians = 15.0 degrees x (pi/180) = 0.2618 radians
2. Substitute the given values into the work formula:
Work = 180 N x 300.0 m x cos(0.2618 radians)
3. Calculate the value of cos(0.2618 radians) using a calculator.
Question 2:
(a) To find the joules and food calories of energy used by the person, we can use the formula:
Energy = Work = Force x Distance
where
Force = 715 N (person's weight)
Distance = 10.5 m (vertical distance)
1. Substitute the given values into the energy formula:
Energy = 715 N x 10.5 m
2. Calculate the value of the energy in joules.
3. To convert from joules to food calories, divide the energy value by 4186 J (1 food calorie = 4186 J).
(b) To find what happened to the other 80% of the food energy, we can subtract the converted energy value from the total food energy consumed by the person.
Question 3:
To find the distance over which the foot must be in contact with the ball, we can use the formula:
Work = Force x Distance
where
Force = 40.0 N (force exerted by the soccer player)
Distance = ?
1. Start with the work-energy principle:
Work = Change in kinetic energy (KE)
Work = (1/2)mv^2 (final kinetic energy) - (1/2)mv^2 (initial kinetic energy)
2. Rearrange the equation to solve for the distance:
Distance = Work / Force
3. Substitute the given values into the distance formula:
Distance = Work / 40.0 N
4. Calculate the value of the distance.
Question 4:
(a) To find the magnitude of momentum and kinetic energy of the car, we can use the formulas:
Momentum = mass x velocity
Kinetic energy = (1/2)mv^2
where
mass = 1200 kg
velocity = 65 mph (convert to SI units)
1. Convert the velocity from mph to m/s by using the conversion factor: 1 mph = 0.44704 m/s.
2. Substitute the given values into the momentum formula to find the magnitude of momentum.
3. Substitute the given values into the kinetic energy formula to find the kinetic energy.
(b) To find the momentum and kinetic energy of the SUV, we can use the same formulas as in part (a), but with the mass of the SUV (2400 kg).
Question 5:
(a) If the cat has momentum magnitude p, then a dog with three times the mass of the cat would have a momentum magnitude of 3p if they have the same speed. Momentum is given by the formula: Momentum = mass x velocity.
(b) If the cat has kinetic energy K, and the dog has the same kinetic energy, we can use the formula: Kinetic energy = (1/2)mv^2, where the mass of the dog is three times the mass of the cat. Rearrange the formula to solve for the velocity v, and substitute the given values to find the magnitude of momentum.
Question 6:
(a) To find the final velocity of the sandwich after the collision, we can use the law of conservation of momentum, which states that the total momentum before the collision is equal to the total momentum after the collision.
(b) To find the mechanical energy dissipated in the collision, we need to calculate the initial and final kinetic energies of the sandwiches and subtract the final kinetic energy from the initial kinetic energy. The mechanical energy is the energy that is lost or transformed during the collision.
Question 7:
(a) To find the impulse the ball gives to the catcher, we can use the formula:
Impulse = Change in momentum = mv (final momentum) - mv (initial momentum)
where
mass = 145 g (convert to kg)
velocity = 36.0 m/s
1. Convert the mass from grams to kilograms.
2. Substitute the given values into the impulse formula.
(b) To find the average force exerted by the ball on the catcher, we can use the formula:
Impulse = Force x Time
where
Impulse = calculated in part (a)
Time = 20 ms (convert to seconds)
1. Convert the time from milliseconds to seconds.
2. Rearrange the formula to solve for the force.
Question 8:
(a) To find the magnitude and direction of the final velocity of each glider after the head-on collision, we can use the law of conservation of momentum, which states that the total momentum before the collision is equal to the total momentum after the collision.
(b) To find the final kinetic energy of each glider, we need to calculate the initial and final kinetic energies and compare the values after the collision. The kinetic energy is the energy associated with the motion of an object.