A shopper in a supermarket pushes a loaded
32 kg cart with a horizontal force of 10 N.
The acceleration of gravity is 9.81 m/s2 .
a) Disregarding friction, how far will the
cart move in 3.3 s, starting from rest?
a = F/m = 10/32 = 0.3125 m/s^2.
a. d = Vo*t + 0.5a*t^2.
d = 0 + 0.5*0.3125*(3.3)^2 = 1.70 m.
To calculate the distance the cart will move, we can use Newton's second law of motion. The equation is given as:
F = m * a
Where:
F = Force applied (10 N)
m = Mass of the cart (32 kg)
a = Acceleration
In this case, the acceleration is the rate at which the cart's velocity increases. Since the cart starts from rest (initial velocity is 0), the acceleration will be equal to the force divided by the mass:
a = F / m
a = 10 N / 32 kg
Let's calculate the acceleration:
a = 0.3125 m/s^2
Now, we can use the kinematic equation to find the distance traveled by the cart:
d = v * t + 0.5 * a * t^2
Where:
d = Distance
v = Initial velocity (0 m/s)
t = Time (3.3 s)
a = Acceleration (0.3125 m/s^2)
Plugging in the values, we can calculate the distance:
d = 0 * 3.3 + 0.5 * 0.3125 * (3.3)^2
d = 0 + 0.5 * 0.3125 * 10.89
d = 1.71094 meters
Therefore, disregarding friction, the cart will move approximately 1.71094 meters in 3.3 seconds starting from rest.
To find out how far the cart will move in 3.3 seconds, we need to use the equations of motion.
First, we need to find the net force acting on the cart by using Newton's second law of motion:
F_net = ma
Where F_net is the net force, m is the mass of the cart, and a is the acceleration of the cart.
Given:
Mass of the cart (m) = 32 kg
Force applied (F) = 10 N
Since the cart starts from rest, its initial velocity (u) is 0 m/s.
Using the equation:
F_net = ma
We can rearrange this equation to solve for acceleration (a):
a = F_net / m
Substituting the given values, we have:
a = 10 N / 32 kg ≈ 0.3125 m/s^2
Now, we can use the equation of motion to find the distance traveled (s) with constant acceleration:
s = ut + 0.5at^2
Where s is the distance traveled, u is the initial velocity (0 m/s), a is the acceleration, and t is the time.
Substituting the given values, we have:
s = 0 + 0.5 * 0.3125 m/s^2 * (3.3 s)^2
Calculating this expression:
s ≈ 0.5 * 0.3125 m/s^2 * 10.89 s^2
s ≈ 1.098 meters
Therefore, disregarding friction, the cart will move approximately 1.098 meters in 3.3 seconds, starting from rest.