1.What is the gravitational force between two trucks, each with a mass of 2.0 x 10^4 kg, that are 2.0 m apart? (G = 6.673 x 10^11 N•m^2/kg^2)
2.Each tire of an automobile has an area of 0.026 m^2 in contact with the ground. The weight of the automobile is 2.6 10^4 N. What is the pressure in the tires?
3.A bowling ball has a mass of 7.0 kg, a moment of inertia of 2.8 × 10^-2 kg·m^2 and a radius of
0.10 m. If it rolls down the lane without slipping at a linear speed of 4.0 m/s, what is its
total kinetic energy?
1. Use Newtons Gravitaional law.
2. Pressure = weight on tire/ area
3. KE = 1/2 mv^2 + 1/2 Iw^2
but w= v/r
so KE= ......
what is the gravitational force between two trucks, each with a mass of 2.0*10^4kg, that are 2.0 m apart?
a motorcycle daredevil is attempting to jump across as many buses as possible. The take off ramp makes an angle18.8dreg above the horizontal, and the landing rampis identical t the take off ramp. The buses are park side by side, and each bus is 2.74m wide. The cyclist leaves the ramp with a speed of v=32.5m/s. What is the maximum number of buses over which the cyclist can jump?
#2 = 250000Pascal
#3 = KE = 1/2 mv^2 + 1/2 Iw^2 = 1/2 (7.0 kg)(32.5 m/s)^2 + 1/2 (2.8 x 10^-2 kg·m^2)(32.5 m/s/0.10 m)^2 = 837.5 J
#4 = The maximum number of buses the cyclist can jump over is equal to the horizontal distance the cyclist can travel divided by the width of each bus. The horizontal distance the cyclist can travel is equal to the initial velocity multiplied by the time it takes for the cyclist to reach the landing ramp. The time it takes for the cyclist to reach the landing ramp is equal to the vertical distance divided by the initial velocity multiplied by the sine of the angle of the ramp. Therefore, the maximum number of buses the cyclist can jump over is equal to (32.5 m/s)((2.74 m/18.8°) / (32.5 m/s)sin(18.8°)) = 8.3 buses.
1. To calculate the gravitational force between two trucks, we can use Newton's law of universal gravitation:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force
G is the gravitational constant (6.673 x 10^11 N·m^2/kg^2)
m1 and m2 are the masses of the trucks (2.0 x 10^4 kg)
r is the distance between the trucks (2.0 m)
Substituting the values into the equation:
F = (6.673 x 10^11 N·m^2/kg^2 * 2.0 x 10^4 kg * 2.0 x 10^4 kg) / (2.0 m)^2
Calculating:
F = 2.6692 x 10^3 N
Therefore, the gravitational force between the two trucks is 2.6692 x 10^3 N.
2. To find the pressure in the tires of an automobile, we can use the formula:
Pressure = weight on tire / area
Given:
Weight of the automobile = 2.6 x 10^4 N
Area of each tire in contact with the ground = 0.026 m^2
Substituting the values into the equation:
Pressure = (2.6 x 10^4 N) / (0.026 m^2)
Calculating:
Pressure = 1 x 10^6 Pa
Therefore, the pressure in the tires of the automobile is 1 x 10^6 Pa or 1,000,000 Pa.
3. To calculate the total kinetic energy of a bowling ball rolling down the lane without slipping, we can use the formula:
KE = 1/2 * mv^2 + 1/2 * I * w^2
Given:
Mass of the bowling ball (m) = 7.0 kg
Moment of inertia (I) = 2.8 x 10^-2 kg·m^2
Radius of the bowling ball (r) = 0.10 m
Linear speed (v) = 4.0 m/s
First, we need to find the angular velocity (w) using the formula:
w = v / r
Substituting the values into the equation:
w = (4.0 m/s) / (0.10 m)
Calculating:
w = 40 rad/s
Now we can substitute the values of mass, velocity, moment of inertia, and angular velocity into the kinetic energy formula:
KE = 1/2 * (7.0 kg) * (4.0 m/s)^2 + 1/2 * (2.8 x 10^-2 kg·m^2) * (40 rad/s)^2
Calculating:
KE = 56 J + 56 J = 112 J
Therefore, the total kinetic energy of the rolling bowling ball is 112 Joules.
For the motorcycle daredevil question, please provide the width of the buses to proceed with the calculation.
1. To find the gravitational force between two trucks, we can use Newton's Law of Universal Gravitation:
F = G * (m1 * m2) / r^2
where F is the gravitational force, G is the gravitational constant (6.673 x 10^11 N•m^2/kg^2), m1 and m2 are the masses of the two trucks, and r is the distance between them.
Plugging in the values given:
m1 = m2 = 2.0 x 10^4 kg
r = 2.0 m
G = 6.673 x 10^11 N•m^2/kg^2
Calculating:
F = (6.673 x 10^11 N•m^2/kg^2) * (2.0 x 10^4 kg * 2.0 x 10^4 kg) / (2.0 m)^2
Simplifying the equation and performing the calculations, the gravitational force between the two trucks is:
F = 2.6704 x 10^6 N
2. To find the pressure in the tires of an automobile, we can use the formula:
Pressure = Weight on tire / Area
Given:
Weight of the automobile = 2.6 x 10^4 N
Area of each tire in contact with the ground = 0.026 m^2
Plugging in the values:
Pressure = (2.6 x 10^4 N) / (0.026 m^2)
Performing the calculations, the pressure in the tires is:
Pressure = 1.0 x 10^6 Pascal
3. To find the total kinetic energy of a bowling ball rolling down the lane without slipping, we can use the formula:
KE = 1/2 * mv^2 + 1/2 * I * w^2
Where KE is the total kinetic energy, m is the mass of the bowling ball, v is the linear speed, I is the moment of inertia, and w is the angular velocity.
Given:
Mass of the bowling ball (m) = 7.0 kg
Moment of inertia (I) = 2.8 x 10^-2 kg·m^2
Radius (r) = 0.10 m
Linear speed (v) = 4.0 m/s
To find the angular velocity (w), we can use the equation:
w = v / r
Plugging in the values and calculating, we can find w:
w = (4.0 m/s) / (0.10 m)
w = 40 rad/s
Now we can substitute the values into the original formula for KE:
KE = 1/2 * (7.0 kg) * (4.0 m/s)^2 + 1/2 * (2.8 x 10^-2 kg·m^2) * (40 rad/s)^2
Performing the calculations, the total kinetic energy of the bowling ball is:
KE = 118.4 Joules
The maximum number of buses the motorcycle daredevil can jump over would require additional information such as the height of the takeoff and landing ramps, the angle of the ramps, and the length of the buses. Without this information, we cannot determine the maximum number of buses the cyclist can jump.