An object with a mass of #4 kg# is moving at #7 m/s# over a surface with a kinetic friction coefficient of #3 #. How much power will it take to accelerate the object at #5 m/s^2?

Question

An object with a mass of #4  kg# is moving at #7 m/s# over a surface with a kinetic friction coefficient of #3 #.  How much power will it take to accelerate the object at #5   m/s^2?

Julia Aguilar · Accepted Answer

The power required is 1000 W.

The frictional force, #F_f#, as the mass slides will be #F_f = mu_k*N = 3 * 4 kg * 9.8 m/s^2 = 117.6 N# We do not know the applied force, but the net force, #F_"net"#, acting on the mass will be #F_"net" = m*a = 4 kg*5 m/s^2 = 20 N# Now we can find the applied force, #F#, #F_"net" = 20 N = F - F_f = F-117.6 N# #F = 117.6 N + 20 N = 137.6 N# Now we can work on finding the power. One of the ways to calculate power, #P#, is #P = F*v# where #v# is velocity. You may be more familiar with power being work done divided by the time required to complete the work. Notice that the units that #P = F*v# will yield on the result would be #N*m/s#. Work done commonly has units of #N*m#. So you see that this formula for power yields the correct units for power. The velocity at the start of this situation is given to be #7 m/s#. So the power is #P = F*v = 137.6 N*7 m/s = 963.2 W# Since the data is has just 1 significant digit, the best answer is 1000 W. (Note that the mass is being accelerated. So the velocity will be continuously increasing. So as time goes on, the power required will be continuously increasing. The question did not specify anything about the length of time that acceleration is to continue.) I hope this helps, Steve

Isabella Alvarez · Answer

undefined To calculate the power required to accelerate the object at 5 m/s^2, we first need to find the force needed to achieve this acceleration. Using Newton's second law (F = ma), where F is the force, m is the mass, and a is the acceleration:

F = ma
F = (4 kg)(5 m/s^2)
F = 20 N

Next, we calculate the force of kinetic friction using the formula:

Frictional force = coefficient of kinetic friction × normal force

The normal force is equal to the weight of the object, which is given by:

Weight = mass × gravitational acceleration
Weight = (4 kg)(9.8 m/s^2)
Weight = 39.2 N

Now, we can calculate the frictional force:

Frictional force = (3)(39.2 N)
Frictional force = 117.6 N

Since the force required to accelerate the object is greater than the force of friction, we only need to consider the force needed for acceleration.

Now, to calculate power, we use the formula:

Power = force × velocity

Where force is the net force acting on the object, which in this case is the force required for acceleration (20 N), and velocity is the speed at which the object is moving (7 m/s).

Power = (20 N)(7 m/s)
Power = 140 watts