note ... find acceleration by using distance
and time (ignore ”incline” ... just treat it like
linear motion of object starting from rest).
A 1.8 kg mass starts from rest and slides
down an inclined plane 8.8×10−1 m long in
0.54 s.
What net force is acting on the mass along
the incline?
Answer in units of N
To find the net force acting on the mass along the incline, we can start by calculating the acceleration of the mass. We can use the formula:
acceleration = (change in velocity) / (change in time)
However, since the mass starts from rest, the initial velocity is 0. Therefore, the change in velocity will be the final velocity.
Given:
Mass (m) = 1.8 kg
Distance (d) = 8.8×10^(-1) m
Time (t) = 0.54 s
We can use the formula:
distance = (initial velocity * time) + (0.5 * acceleration * time^2)
Since the mass starts from rest, the initial velocity is 0. Therefore, the formula becomes:
distance = 0 + (0.5 * acceleration * time^2)
8.8×10^(-1) = 0.5 * acceleration * (0.54)^2
Now, rearrange the equation to solve for acceleration:
acceleration = (8.8×10^(-1)) / (0.5 * (0.54)^2)
Simplifying:
acceleration = (8.8×10^(-1)) / (0.5 * 0.2916)
acceleration = (8.8×10^(-1)) / 0.1458
acceleration ≈ 6.03 m/s^2
Next, we can calculate the net force acting on the mass using Newton's second law of motion:
force = mass * acceleration
force = 1.8 kg * 6.03 m/s^2
Calculating:
force ≈ 10.854 N
Therefore, the net force acting on the mass along the incline is approximately 10.854 N.
To find the net force acting on the mass along the incline, we need to 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.
To find the acceleration, we can use the equation of motion for an object sliding down an inclined plane.
The equation is given by:
s = ut + (1/2)at^2
Where:
- s is the distance traveled (8.8x10^-1 m in this case)
- u is the initial velocity (0 since the object starts from rest)
- a is the acceleration (which we need to find)
- t is the time taken (0.54 s in this case)
Rearranging the equation, we get:
s = (1/2)at^2
Multiplying both sides by 2/a and simplifying, we have:
2s/a = t^2
Now, substitute the given values:
2(8.8x10^-1)/a = (0.54)^2
Simplifying further, we get:
a = 2(8.8x10^-1)/(0.54)^2
a ≈ 2.583 m/s^2
Now that we have the acceleration, we can calculate the net force:
Using Newton's second law, F = ma:
F = (1.8 kg) * (2.583 m/s^2)
F ≈ 4.649 N
Therefore, the net force acting on the mass along the incline is approximately 4.649 N.