A body of mass 5.0kg slides from rest down a plane inclined at 30degrees to the horizontal. After sliding 12m down the plane it is found to have a speed of 10m/s.
a) How much work has been done in overcoming friction along the plane?
b) Calculate the average value of the force of friction.
Try using conservation of energy.
Work done against friction = PE loss - KE gain
W = M*g*(12 sin30) - (M/2)(10^2)
= 44 J
Average friction force = W/12 m = 3.67 N
To determine the answers to these questions, we can use the principles of work and energy. Here's how you can calculate the values:
a) To find the work done in overcoming friction along the plane, we need to consider the change in kinetic energy of the body. The work done by friction is equal to the change in kinetic energy.
The initial velocity of the body is zero as it starts from rest. The final velocity is given as 10 m/s. The mass of the body is 5.0 kg.
The change in kinetic energy (ΔKE) is calculated using the formula:
ΔKE = 0.5 * m * (vf^2 - vi^2)
Substituting the given values:
ΔKE = 0.5 * 5.0 kg * (10 m/s)^2
Simplifying, we get:
ΔKE = 0.5 * 5.0 kg * 100 m^2/s^2
ΔKE = 250 Joules
Therefore, the work done in overcoming friction along the plane is 250 Joules.
b) To calculate the average value of the force of friction, we can use the equation:
Work = Force * Distance
The work done by friction is 250 Joules, and the distance traveled is 12 meters.
Substituting the values into the equation, we have:
250 Joules = Force * 12 meters
To find the average value of the force of friction, we divide both sides of the equation by 12 meters. This gives us:
Force = 250 Joules / 12 meters
Calculating the value, we get:
Force ≈ 20.8 Newtons
Therefore, the average value of the force of friction is approximately 20.8 Newtons.