HELP! I'm doing a webassign, and am completley lost on these problems. If you could help with any, that would be great.
A crate weighing 9.40 103 N is pulled up a 36° incline by a force parallel to the plane. If the coefficient of kinetic friction between the crate and the surface of the plane is 0.750, what is the magnitude of the applied force required to move the crate at a constant velocity?
A 125 m long ramp is to be built for a ski jump. If a skier starting from rest at the top is to have a speed no faster than 27 m/s at the bottom, what should be the maximum angle of inclination?
While catching a baseball that is traveling horizontally at a speed of 12 m/s, a player's glove and arm move straight backward 25 cm from the time of contact to the time the ball comes to rest. If the ball has a mass of 0.20 kg, what is the average force on the ball during that interval?
Sure, I'd be happy to help you with these problems!
Problem 1: Magnitude of Applied Force
To find the magnitude of the applied force required to move the crate at a constant velocity, we need to consider the forces acting on the crate. We have the weight of the crate acting straight down, which can be calculated using the formula w = mg, where m is the mass of the crate and g is the acceleration due to gravity. Since weight is a force, we also need to convert it to Newtons by multiplying it by the acceleration due to gravity.
Next, we have the force of kinetic friction, which can be calculated using the formula f = μN, where μ is the coefficient of kinetic friction and N is the normal force. The normal force is the perpendicular force exerted by the inclined plane on the crate. It can be calculated using the formula N = mgcosθ, where θ is the angle of inclination.
Finally, we have the applied force, which is parallel to the inclined plane.
To find the magnitude of the applied force, we need to set up the equation of forces:
Applied force - Force of kinetic friction - Weight(sinθ) = 0
Now we can substitute the values we know into the equation and solve for the applied force.
Problem 2: Maximum Angle of Inclination
To find the maximum angle of inclination for the ramp, we need to consider the conservation of energy. At the top of the ramp, the skier has only potential energy, and at the bottom, the skier has both potential and kinetic energy.
We can use the formula for potential energy, PE = mgh, where m is the mass of the skier, g is the acceleration due to gravity, and h is the height of the ramp at the top.
At the bottom of the ramp, the skier has both potential and kinetic energy. The kinetic energy can be calculated using the formula KE = 1/2mv^2, where v is the velocity of the skier at the bottom.
Since energy is conserved, we can equate the potential energy at the top to the sum of the potential and kinetic energy at the bottom. Now we can solve for the maximum angle of inclination using the given values.
Problem 3: Average Force on the Ball
To find the average force on the ball during the interval, we can apply the impulse-momentum principle. The impulse is given by the change in momentum and can be calculated using the formula I = Δp = mΔv, where m is the mass of the ball and Δv is the change in velocity.
We know that the ball comes to rest, so the change in velocity is equal to the initial velocity of the ball. We can find the initial velocity using the given speed of the ball.
Once we have the impulse, we can calculate the average force using the formula F_avg = I/Δt, where Δt is the time interval over which the force is applied.
In this case, we are given the distance the player's glove and arm moves backward, but we need to convert it to a time interval using the speed of the ball.
Now we can substitute the known values into the equation and solve for the average force on the ball.
I hope this explanation helps you understand how to approach these problems. Let me know if you have any questions about the specific steps or calculations!