A crate with a mass of (111.5) kg is lifted by a crane. If the crate is accelerating upward at (2.7) m/s2, what is the tension in the cable? Give your answer in newtons (N) and with 3 significant figures.
To find the tension in the cable, 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.
The net force is the difference between the tension in the cable and the force due to gravity acting on the crate. The force due to gravity can be calculated by multiplying the mass of the crate by the acceleration due to gravity.
So, let's calculate the force due to gravity acting on the crate:
Force due to gravity = mass of the crate × acceleration due to gravity
Force due to gravity = 111.5 kg × 9.8 m/s^2
Force due to gravity = 1092.7 N
Now, let's calculate the net force:
Net force = mass of the crate × acceleration
Net force = 111.5 kg × 2.7 m/s^2
Net force = 300.9 N
Since the net force is equal to the tension in the cable minus the force due to gravity, we can set up the equation:
Tension - Force due to gravity = Net force
Tension - 1092.7 N = 300.9 N
Now, let's solve for the tension:
Tension = 300.9 N + 1092.7 N
Tension = 1393.6 N
Therefore, the tension in the cable is 1393.6 N, rounded to 3 significant figures.
To find the tension in the cable, we can use Newton's second law of motion, which tells us that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
The equation for Newton's second law is:
F = m * a
Where:
F is the net force in newtons (N)
m is the mass of the object in kilograms (kg)
a is the acceleration of the object in meters per second squared (m/s²)
In this case, the crate has a mass of 111.5 kg and is accelerating upward at 2.7 m/s². Plugging these values into the equation, we get:
F = 111.5 kg * 2.7 m/s²
Calculating this gives us the tension in the cable:
F = 300.45 N
Rounding to 3 significant figures, the tension in the cable is approximately 300 N.