Question

a student is standing in an elevator that is accelerating downward. the force that the student exerts on the floor of the elevator must be
(1) less than the weight of the student when at rest
(2) greater than the weight of the student when at rest
(3) less than the force of the floor on the student
(4) greater than the force of the floor on the student
12.
two forces act concurrently on an object on a horizontal, frictionless surface, as shown in the diag below.
what additional force, when applied to the object, will establish equilibrium?
(1) 16 n toward the right
(2) 16 n toward the left
(3) 4 n toward the right
(4) 4 n toward the left

Explanation:

Step1: Calculate the net force

The forces acting on the object are \(F_1 = 10\space N\) (right) and \(F_2=6\space N\) (left). The net force \(F_{net}\) is \(F_{net}=F_1 - F_2\) (taking right as positive).

$$ F_{net}=10 - 6=4\space N\space(\text{toward the right}) $$

Step2: Determine the force for equilibrium

For equilibrium, the additional force \(F_{add}\) must be such that \(F_{net}+F_{add} = 0\). Let \(F_{add}=x\). Then \(4 + x=0\), so \(x=- 4\space N\). A negative sign (since we took right as positive) means the force is toward the left.

Answer:

(4) \(4\space N\) toward the left