An 8.0 kg bag of coin is being pulled upward by a rope rises 20.0 cm in 0.50 sec, starting from rest. Assuming the acceleration is constant, calculate the net force on the bag. what is the upward force on the bag exerted by the rope?
The net force F is what accelerates the bag. Use F = ma to calculate it. You will need the accleration , a. For that, use
X = 0.2 m = (1/2) a (0.5)^2
The force exerted by the rope, f, is
F + mg, since the net force is
F = f - mg,
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To solve this problem, we need to use the equations of motion. Specifically, we will use the equation:
Δy = v₀t + (1/2)at²
where Δy is the displacement, v₀ is the initial velocity, t is the time, and a is the acceleration.
Given:
Mass of the bag (m) = 8.0 kg
Initial velocity (v₀) = 0 m/s (since the bag starts from rest)
Displacement (Δy) = 20.0 cm = 0.20 m
Time (t) = 0.50 s
First, let's calculate the acceleration (a):
Δy = v₀t + (1/2)at²
0.20 = 0.5 * a * (0.50)²
0.20 = 0.125a
a = 0.20 / 0.125
a ≈ 1.6 m/s²
Next, let's calculate the net force (Fnet):
Fnet = ma
Fnet = 8.0 kg * 1.6 m/s²
Fnet ≈ 12.8 N
Therefore, the net force on the bag is approximately 12.8 N.
To find the upward force exerted by the rope on the bag, we need to consider the weight of the bag. The weight (W) is given by the equation:
W = mg
where m is the mass and g is the acceleration due to gravity (approximately 9.8 m/s²).
W = 8.0 kg * 9.8 m/s²
W ≈ 78.4 N
Since the bag is being pulled upward, the rope needs to exert a force equal to the weight plus the net force acting on it.
Upward force on the bag by the rope = Fnet + W
Upward force on the bag by the rope ≈ 12.8 N + 78.4 N
Upward force on the bag by the rope ≈ 91.2 N
Therefore, the upward force on the bag exerted by the rope is approximately 91.2 N.
To calculate the net force on the bag and the upward force exerted by the rope, we need to 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.
Step 1: Calculate the acceleration of the bag.
Given:
Mass of the bag (m) = 8.0 kg
Change in height (Δh) = 20.0 cm = 0.20 m (converted to meters)
Time taken (Δt) = 0.50 sec
We can use the equation for accelerated motion in the vertical direction (assuming no other forces are acting):
Δh = (1/2) * a * Δt^2
Rearranging the equation to solve for acceleration:
a = 2 * Δh / Δt^2
Substituting the values:
a = 2 * 0.20 m / (0.50 sec)^2
Step 2: Calculate the net force on the bag.
Using Newton's second law:
Net force (F) = m * a
Substituting the values:
F = 8.0 kg * (result from step 1)
This will give you the net force acting on the bag.
Step 3: Calculate the upward force exerted by the rope.
Since the bag is being pulled upward by the rope, the upward force exerted by the rope will be equal to the net force on the bag.
So, the net force and the upward force exerted by the rope will have the same value.
Calculate the value of F (net force) in step 2 to get the answer to both parts of the question.