A block of mass 4.0 kg, which has an initial speed of 6.0 m/s, slides on a horizontal surface and eventually comes to rest from friction.
a. Calculate the work that must be done by friction on the block to bring it to rest.
b. If the friction force between the block and the surface has a magnitude of 88 N, how far will the block travel before stopping?
a. the work is equal to the initial kinetic energy of the block
... K.E. = 1/2 m v^2 = 1/2 * 4.0 kg * (6.0 m/s)^2 = ? Joules
b. work = force * distance
... distance = (answer a.) / 88 N = ? m
To answer these questions, we need to use the concepts of work and energy.
a. To calculate the work done by friction, we first need to determine the initial kinetic energy and the final kinetic energy of the block. The work done by friction is equal to the change in kinetic energy.
The initial kinetic energy of the block is given by the formula:
K_initial = (1/2) * mass * speed^2
Substituting the given values:
K_initial = (1/2) * 4.0 kg * (6.0 m/s)^2
The final kinetic energy of the block is zero since it comes to rest. Therefore, K_final = 0.
The work done by friction is given by the formula:
Work = K_final - K_initial
Substituting the values:
Work = 0 - [(1/2) * 4.0 kg * (6.0 m/s)^2]
Simplifying the expression:
Work = - (1/2) * 4.0 kg * 36.0 m^2/s^2
Work = - 72.0 Joules
Therefore, the work done by friction on the block to bring it to rest is -72.0 Joules.
b. To calculate the distance traveled by the block before stopping, we can use the work-energy principle. The work done on the block by friction is equal to the force of friction multiplied by the distance traveled. Therefore:
Work = force * distance
Solving for distance:
distance = Work / force
Substituting the values:
distance = -72.0 Joules / 88 N
distance ≈ -0.82 meters
Since distance cannot be negative, we take the absolute value of the answer. Therefore, the block will travel approximately 0.82 meters before stopping.