Question

QUESTION 3
Suppose you have a 100-kg wooden crate resting on a wood floor. Assume that the maximum force you can exert horizontally on the crate without moving it
is 588 N. If you continue to exert this force once the crate starts to move, what will be the magnitude of its acceleration (in m/s 22 Note: Use Table 5.1
in
Chapter 5 to determine the coefficient of friction for this problem.

Wood on wood static friction = 0.5
Wood on wood kinetic friction = 0.3

Answer 1

The force of frictions is opposed to relative motion.

The acceleration of the crate is approximately 2.937 m/s².

Reason:

The given parameters are;

The mass of the wood, m = 100 kg

The force which can move the wood, F = 588 N

Wood on wood static friction, $\mu_s$ = 0.5

Wood on wood kinetic friction, $\mu_k$ = 0.3

Solution;

The force of friction, $F_f$, acting when the crate is moving is given as

follows;

$F_f$ = m × g × $\mu_k$

Where;

g = The acceleration due to gravity ≈ 9.81 m/s²

Therefore, we have;

$F_f$ = 100 × 9.81 × 0.3 = 294.3

The force of friction, $F_f$ = 294.3 N

The force with which the crate moves, F = 588 - 294.3 = 293.7

The force with which the crate moves, F = 293.7 N

Force = Mass, m × Acceleration, a

$a = \dfrac{F}{m}$

Therefore;

$a = \dfrac{293.7 \ N}{100 \ kg} = 2.937$

The acceleration of the crate, a ≈ 2.937 m/s².

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