First, we need to calculate the force needed to accelerate the block to 20 m/s in 5 seconds. We can use the equation:
F = ma
Where F is the force, m is the mass of the block (10 kg), and a is the acceleration. We can calculate the acceleration using the equation:
a = (vf - vi) / t
Where vf is the final velocity (20 m/s), vi is the initial velocity (0 m/s), and t is the time (5 seconds).
a = (20 m/s - 0 m/s) / 5 s = 4 m/s^2
Now we can calculate the force:
F = 10 kg * 4 m/s^2 = 40 N
Next, we need to calculate the frictional force acting against the motion of the block. The frictional force can be calculated using the equation:
f = μN
Where μ is the coefficient of kinetic friction (0.57) and N is the normal force. The normal force can be calculated as the weight of the block:
N = mg = 10 kg * 9.8 m/s^2 = 98 N
Now we can calculate the frictional force:
f = 0.57 * 98 N = 55.86 N
Since the frictional force is acting in the opposite direction of the force needed to accelerate the block, we need to subtract it from the force we calculated earlier:
F_net = F - f = 40 N - 55.86 N = -15.86 N
The negative sign indicates that the net force is acting in the opposite direction of motion.
Finally, we can calculate the power needed to supply this net force using the equation:
P = F_net * v
Where P is power, F_net is the net force, and v is velocity (20 m/s).
P = -15.86 N * 20 m/s = -317.2 W
The average power must be supplied to push the block from rest to 20 m/s in 5 seconds against a frictional force of 55.86 N is -317.2 W.
1. What average power must be supplied to push a 10kg block from rest to 20m/s in 5 seconds when the cremeient of kinetic friction bit the block and surface is 0.57.
1 answer