A net force of 75 lbs acts on a body of mass 25 slugs which is initially at rest. Find its acceleration. How fast will the body be moving 12 seconds later? Please indicate the formula used.
To find the acceleration of an object, you can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by the acceleration.
The formula you can use is:
F = m * a
Where:
F is the net force acting on the object, which is given as 75 lbs.
m is the mass of the object, which is given as 25 slugs.
a is the acceleration of the object (what we're trying to find).
To solve for acceleration (a), rearrange the formula:
a = F / m
Now, substitute the given values into the formula:
a = 75 lbs / 25 slugs
Since both pounds and slugs are units of force, they cancel each other out, leaving you with:
a = 3 slugs
Therefore, the acceleration of the body is 3 slugs.
To find how fast the body will be moving after 12 seconds, you can use the equation of motion:
v = u + a * t
Where:
v is the final velocity.
u is the initial velocity, which is 0 since the body is initially at rest.
a is the acceleration, which we found to be 3 slugs.
t is the time, which is given as 12 seconds.
Substituting the values into the formula:
v = 0 + 3 slugs * 12 seconds
v = 36 slugs * seconds
Therefore, the body will be moving at a speed of 36 slugs per second after 12 seconds.
To find the acceleration of the body, we can use Newton's second law of motion, which is given by the formula: F = ma, where F is the net force acting on the body, m is the mass of the body, and a is the acceleration.
Given:
Net force (F) = 75 lbs
Mass (m) = 25 slugs
We need to convert the force from pounds to slugs by dividing by the acceleration due to gravity, which is approximately 32.2 ft/s^2. The conversion factor from pounds to slugs is 1 slug = 32.2 lbs/g (where g is the acceleration due to gravity).
Converting the force to slugs:
75 lbs / (32.2 lbs/g) = 2.330 slugs
Using F = ma, we can rearrange the formula to solve for acceleration:
a = F / m
Plugging in the values:
a = 2.330 slugs / 25 slugs = 0.0932 ft/s^2
Therefore, the acceleration of the body is approximately 0.0932 ft/s^2.
To find the final velocity of the body after 12 seconds, we can use the formula of motion: v = u + at, where:
v = final velocity
u = initial velocity (which is 0 since the body is initially at rest)
a = acceleration
t = time
Plugging in the values:
v = 0 + (0.0932 ft/s^2) × (12 s)
v = 1.1184 ft/s
Therefore, the body will be moving at a speed of approximately 1.1184 ft/s after 12 seconds.