A 90.0 N grocery cart is pushed 14.0 m along an aisle by a shopper who exerts a constant horizontal force of 40.0 N. If all frictional forces are neglected and the cart starts from rest, what is the grocery cart's final speed?
mg = 90 N.
m = 90 / 9.8 = 9.18 kg = Mass of cart.
a = Fap / m = 40 / 9.18 = 4.36 m/s^2.
Vf^2 = Vo^2 + 2a*d,
Vf^2 = 0 + 8.71*14 = 121.96,
Vf = 11.0 m/s.
Well, let me do some quick calculations here. With a force of 40.0 N and neglecting friction, the net force on the cart is 40.0 N. Using Newton's second law, we can calculate the acceleration. Since the mass of the cart is not given, we can't determine the final speed. It seems like the grocery cart has decided to shop incognito and hide its mass from us. I guess the final speed will remain a mystery, just like the secret ingredient in grandma's famous cookies. They'll always leave you guessing!
To find the grocery cart's final speed, we can use the work-energy principle. According to this principle, the work done on an object is equal to the change in its kinetic energy.
The work done on the cart is given by the force applied multiplied by the distance moved:
Work = Force × Distance
W = F × d
Substituting the given values:
W = 40.0 N × 14.0 m
W = 560 N·m
Since the cart starts from rest, its initial kinetic energy is zero. Therefore, the change in kinetic energy is given by the work done on the cart.
Change in kinetic energy = Work
ΔKE = W
The change in kinetic energy is also given by the formula:
ΔKE = (1/2)mv^2
Where m is the mass of the cart and v is its final velocity.
Substituting the given force value (90.0 N) as the weight of the cart, we can find its mass using the equation:
Weight = mass × acceleration due to gravity
90.0 N = m × 9.8 m/s^2
m = 9.18 kg
Now we can solve for the final velocity:
ΔKE = (1/2)mv^2
560 N·m = (1/2)(9.18 kg) v^2
1120 N·m = 9.18 kg v^2
v^2 = 122.14 m^2/s^2
v ≈ 11.05 m/s
Therefore, the grocery cart's final speed is approximately 11.05 m/s.
To find the final speed of the grocery cart, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
First, let's find the acceleration of the cart using the formula:
F = m * a
where F is the net force, m is the mass of the cart, and a is the acceleration. Solving for a, we have:
a = F / m
Given that the force (F) exerted by the shopper is 40.0 N, and the mass (m) of the cart is not provided, we need to find the mass of the cart.
We know that weight (W) is equal to the mass (m) of an object multiplied by the gravitational acceleration (g). In this case, the weight of the cart is given as 90.0 N. So we have:
W = m * g
Rearranging the formula, we can solve for mass:
m = W / g
where g is the acceleration due to gravity, which is approximately 9.8 m/s^2.
Substituting the given values:
m = 90.0 N / 9.8 m/s^2 = 9.18 kg (rounded to two decimal places)
Now that we have the mass of the cart, we can substitute it back into the equation to find the acceleration:
a = 40.0 N / 9.18 kg = 4.35 m/s^2 (rounded to two decimal places)
Now, we can use one of the kinematic equations to find the final speed of the cart. The equation we can use is:
v^2 = v0^2 + 2 * a * d
where v is the final speed, v0 is the initial speed (which is zero since the cart starts from rest), a is the acceleration, and d is the distance.
Since the initial speed is zero and all frictional forces are neglected, the equation simplifies to:
v^2 = 2 * a * d
Substituting the values we know:
v^2 = 2 * 4.35 m/s^2 * 14.0 m
v^2 = 121.8 m^2/s^2
Finally, we take the square root of both sides of the equation to find the final speed of the grocery cart:
v = √(121.8 m^2/s^2) = 11.04 m/s (rounded to two decimal places)
Therefore, the final speed of the grocery cart is approximately 11.04 m/s.