Question

an 8.00 kg block of ice, released from rest at the top of a 1.50-m-long frictionless ramp, slides downhill, reaching a speed of 2.50 m>s at the bottom. (a) what is the angle between the ramp and the horizontal? (b) what would be the speed of the ice at the bottom if the motion were opposed by a constant friction force of 10.0 n parallel to the surface of the ramp?

Answer 1

The angle between the ramp and the horizontal is approximately 15.9°. The speed of the ice at the bottom would be less than 2.50 m/s if there was a friction force of 10.0 N parallel to the surface of the ramp.

Step-by-step explanation:

a) Finding the angle between the ramp and the horizontal:

To find the angle, we can use trigonometry. The acceleration down the ramp is equal to the gravitational acceleration times the sine of the angle, so the angle can be found using the equation sinθ = a/g. Plugging in the values, we get sinθ = 2.50/9.8, which gives us θ ≈ 15.9°.

b) Finding the speed of the ice at the bottom with friction:

When the motion is opposed by friction, we need to subtract the friction force from the net force to find the acceleration. The friction force is given as 10.0 N, so the net force is the force of gravity minus the friction force. Using this net force, we can calculate the acceleration and then find the speed at the bottom using the equations of motion. The speed at the bottom would be less than 2.50 m/s, due to the opposing friction force.