Question

A student produces a power of p = 0.87 kw while pushing a block of mass m = 75 kg on an inclined surface making an angle of θ = 8.5 degrees with respect to the horizontal. the coefficient of kinetic friction between the block and the incline is μk = 0.16. randomized variables p = 0.87 kw m = 75 kg θ = 8.5 degrees μk = 0.16 50% part (a) write an expression for the maximum constant speed, vm, the block travels at under the power applied by the student.

Answer 1

When block is pushed upwards along the inclined plane

the net force applied on the block will be given as

$F_{net} = mg sin\theta + \mu_k mg cos\theta$

here we know that

m = 75 kg

$\theta = 8.5 degree$

$\mu_k = 0.16$

now plug in all values into this

$F_{net} = 75\times 9.8 sin8.5 + 0.16 \times 75\times 9.8 cos8.5$

$F = 225 N$

now for finding the power is given as

$P = Fv$

$0.87 \times 10^3 = 225 \time v$

$v = \frac{870}{225} = 3.87 m/s$