A shopper in a supermarket pushes a loaded
cart with a horizontal force of 13 N. The cart
has a mass of 36 kg.
The acceleration of gravity is 9.8 m/s
2
.
Disregarding friction, how far will the cart
move in 4.5 s, starting from rest?
Answer in units of m
To find the distance the cart will move, we can use the equation of motion:
distance = initial velocity * time + (1/2) * acceleration * time^2
Given data:
Force applied (F) = 13 N
Mass of the cart (m) = 36 kg
Acceleration due to gravity (g) = 9.8 m/s^2
Time (t) = 4.5 s
First, let's find the acceleration of the cart using Newton's second law:
Force = mass * acceleration
13 N = 36 kg * acceleration
Solving for acceleration:
acceleration = 13 N / 36 kg
acceleration ≈ 0.3611 m/s^2
Now, we can find the initial velocity of the cart using the kinematic equation:
initial velocity = acceleration * time
initial velocity = 0.3611 m/s^2 * 4.5 s
initial velocity ≈ 1.6249 m/s
Finally, we can calculate the distance the cart will move using the equation of motion:
distance = initial velocity * time + (1/2) * acceleration * time^2
distance = 1.6249 m/s * 4.5 s + (1/2) * 0.3611 m/s^2 * (4.5 s)^2
distance ≈ 7.3118 m
Therefore, the cart will move approximately 7.3118 meters in 4.5 seconds, starting from rest.
To calculate the distance the cart will move, we can use Newton's second law of motion, which states that the acceleration of an object is equal to the net force acting on it divided by its mass:
a = F/m
In this case, since we are disregarding friction, the only force acting on the cart is the horizontal force applied by the shopper, which is 13 N. The mass of the cart is 36 kg. Therefore, we can calculate the acceleration:
a = F/m = 13 N / 36 kg ≈ 0.361 m/s²
Now that we have the acceleration, we can use the equation of motion to find the distance traveled by the cart. The equation relates displacement, initial velocity, acceleration, and time:
d = v₀t + (1/2)at²
However, in this case, the cart starts from rest, so the initial velocity v₀ is 0 m/s. Therefore, the equation simplifies to:
d = (1/2)at²
Plugging in the values, we have:
d = (1/2) * 0.361 m/s² * (4.5 s)²
Simplifying further:
d = (1/2) * 0.361 m/s² * 20.25 s²
d ≈ 3.663 m
Therefore, the cart will move approximately 3.663 meters in 4.5 seconds, starting from rest.
F = m*a = 13 N.
36*a = 13
a = 0.361 m/s^2
d = 0.5a*t^2 = 0.5*0.361*4.5^2 = 3.66 m.