A 2.50-kg object is moving along the x -axis at 1.60 m/s. As it S S passes the origin, two forces F 1 and F 2 are applied, both in the y -direction (plus or minus). The forces are applied for 3.00 s, after S which the object is at x S = 4.80 m, y = 10.8 m. If F 1 = 15.0 N, what’s F 2 ?
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To solve this problem, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration.
Since the object is moving along the x-axis, the only force component that will affect the object's motion in the x-direction is due to the friction force, which we can assume is negligible.
We can split the given force F1 into its x-component and y-component. The x-component of F1 does not affect the object's motion in the x-direction, so we only need to consider the y-component of F1. Given that F1 = 15.0 N, we can find its y-component as follows:
F1y = F1 * sin(θ)
F1y = 15.0 N * sin(90°)
F1y = 15.0 N
Now, let's consider the y-direction motion of the object. We can apply the equation of motion for an object under constant acceleration:
y = y0 + v0y * t + (1/2) * a_y * t^2
Where:
- y is the final y-coordinate (10.8 m)
- y0 is the initial y-coordinate (0 m)
- v0y is the initial velocity in the y-direction (0 m/s, as it was moving along the x-axis)
- t is the time interval (3.00 s)
- a_y is the acceleration in the y-direction (unknown)
- (1/2) * a_y * t^2 is the change in position due to the acceleration
Substituting the known values, we can solve for a_y:
10.8 m = 0 m + 0 m/s * 3.00 s + (1/2) * a_y * (3.00 s)^2
10.8 m = (1/2) * a_y * 9.00 s^2
a_y = (10.8 m) / (4.50 s^2)
a_y = 2.4 m/s^2
Now that we have the acceleration in the y-direction, we can use Newton's second law to find F2. The net force in the y-direction is equal to the mass of the object times the acceleration in the y-direction:
F_net_y = m * a_y
F1y + F2 = m * a_y
15.0 N + F2 = 2.50 kg * 2.4 m/s^2
F2 = (2.50 kg * 2.4 m/s^2) - 15.0 N
F2 = 6.0 N - 15.0 N
F2 = -9.0 N
Therefore, F2 is equal to -9.0 N. The negative sign indicates that the force F2 is in the opposite direction of the positive y-axis.
To find the value of F2, we can use the laws of motion and the information provided in the question. Let's break down the problem step by step:
Step 1:
First, let's understand the situation and the forces acting on the object. The object is initially moving along the x-axis with a velocity of 1.60 m/s. As it passes the origin, two forces, F1 and F2, are applied in the y-direction.
Step 2:
Next, let's determine the acceleration of the object during the time when the forces are applied. According to Newton's second law of motion, the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma). Since only forces in the y-direction are applied, the net force in the x-direction will be zero.
Step 3:
Since the forces are applied for 3.00 seconds and the object was initially moving in the x-direction, we can use the equation of motion to find the acceleration in the y-direction. The equation is: y = y0 + v0y*t + (1/2) * ay * t^2, where y0 is the initial position, v0y is the initial velocity in the y-direction, t is the time, and ay is the acceleration in the y-direction.
Since the object is initially at the origin and has no initial velocity in the y-direction (v0y = 0), we can simplify the equation to: y = (1/2) * ay * t^2.
We plug in the given values: y = 10.8 m, t = 3.00 s. Solving for ay, we get: ay = (2 * y) / t^2.
Step 4:
Now that we have the acceleration in the y-direction, we can calculate the net force in the y-direction (Fnety). Since Fnety = may according to Newton's second law, we use the equation: Fnety = m * ay.
Given that the mass of the object is 2.50 kg, we can substitute the values and get the net force in the y-direction.
Step 5:
Finally, we can determine the value of F2 by subtracting F1 from the calculated net force in the y-direction (F2 = Fnety - F1).
By following these steps, we can find the value of F2.
determine the net y force.
10.8m=a*t=(netforcey/mass)*time
solve fodr netforceinY direction
then, F2=NetforceinY - F1