Question

A child leaves her book bag on a slide. The bag, which is at the top of the slide, starts from rest and reaches the bottom in 1.57 s. The mass of the book bag is 2.05 kg, the length of the slide is 3.70 m and the angle of incline is 35.0°. (Assume the +x-axis to be parallel to and down the slide. For all values, enter the magnitude only.) With what acceleration (in m/s²) does the bag

Answer 1

The acceleration of the book bag that slides down the incline is calculated using the distance it travels and the time it takes to reach the bottom, resulting in an acceleration of 1.50 m/s².

Step-by-step explanation:

To determine the acceleration of the book bag as it slides down the incline, we can use the kinematic equation for uniformly accelerated motion, which relates the initial velocity, final velocity, distance traveled, time, and acceleration. The initial velocity (v_i) is 0 since the bag starts from rest. We are not directly given the final velocity, but we do not need it for this equation. Instead, we focus on the distance (d) which is the length of the slide and the time (t) it took for the book bag to slide down.

To find the acceleration (a), we can use the formula:

d = v_i * t + ½ * a * t^2

We have: d = 3.70 m, v_i = 0 m/s (starting from rest), and t = 1.57 s. Plugging these values into the equation, we get:

3.70 m = (0 m/s) * (1.57 s) + ½ * a * (1.57 s)^2

Solving for a gives us:

Acceleration (a) = ½ * (3.70 m) / (1.57 s)^2 = 1.50 m/s²