a plane inclined at an angle of 30 degrees to the horizontal has an efficiency of 50% what is the force required to push a load of 120N up the plane
To find the force required to push the load up the inclined plane, we need to use the formula for the force needed to overcome gravity on an inclined plane:
Force = Load * Sin(angle)
Where:
- Force is the force required to push the load up the plane
- Load is the weight of the load (in this case, 120N)
- Sin(angle) is the sine of the angle of inclination (in this case, 30 degrees)
Let's calculate the force required step by step:
1. Calculate the sine of the angle (30 degrees):
Sin(30) ≈ 0.5
2. Substitute the values into the formula:
Force = 120N * 0.5
3. Solve the equation:
Force = 60N
Therefore, the force required to push a load of 120N up an inclined plane with an angle of 30 degrees is 60N.
To find the force required to push the load up the plane, we need to calculate the component of the weight of the load that acts parallel to the inclined plane.
First, let's find the weight of the load. The weight is given as 120N.
The weight of an object is the force acting on it due to gravity, which is given by the formula:
Weight = mass * acceleration due to gravity
To find the weight, we need to know the mass of the load and the acceleration due to gravity. The acceleration due to gravity is approximately 9.8 m/s².
Weight = 120N
120N = mass * 9.8 m/s²
Dividing both sides of the equation by 9.8 m/s², we get:
mass = 120N / 9.8 m/s²
mass = 12.24 kg
Now that we know the mass of the load is 12.24 kg, we can calculate the component of its weight that acts parallel to the inclined plane. This component is given by the formula:
Parallel Force = Weight * sin(angle of inclination)
Plugging in the values:
Parallel Force = 12.24 kg * 9.8 m/s² * sin(30 degrees)
Parallel Force = 12.24 kg * 9.8 m/s² * 0.5
Parallel Force = 60.18 N (rounded to two decimal places)
Therefore, the force required to push the load of 120N up the inclined plane is approximately 60.18N.
To find the force required to push a load up an inclined plane, we need to determine the component of the weight of the load acting parallel to the inclined plane. This can be done by calculating the weight of the load and then multiplying it by the sine of the angle of inclination.
First, let's find the weight of the load. The weight (W) can be calculated using the formula:
W = mass * acceleration due to gravity
We don't have the mass of the load, but we know its weight is 120N. Since weight is a force and force is equal to mass multiplied by acceleration, we can write:
120N = mass * 9.8 m/s²
Dividing both sides of the equation by 9.8 m/s², we get:
mass = 120N / 9.8 m/s²
mass ≈ 12.24 kg
Now that we have the mass of the load, we can find the force required to push it up the inclined plane. The force required (F) can be calculated using the formula:
F = m * g * sin(θ)
where m is the mass, g is the acceleration due to gravity, and θ is the angle of inclination.
Plugging in the known values:
F = 12.24 kg * 9.8 m/s² * sin(30°)
To find the sine of 30 degrees, you can use a scientific calculator or look up the value in a trigonometric table. The sine of 30 degrees is approximately 0.5.
F ≈ 12.24 kg * 9.8 m/s² * 0.5
F ≈ 60.04 N
Therefore, the force required to push a load of 120N up the inclined plane is approximately 60.04 N.