Question

a 70-kg stunt artist rides in a rocket sled which slides along a flat inclined surface. at an instant when the sled's acceleration has a horizontal component of 6.0 m/s2 and a downward component of 2.8 m/s2, what is the magnitude of the force on the rider by the sled?

Answer 1

The magnitude of the force on the rider by the sled is 464 N.

Step-by-step explanation:

The force on the rider by the sled can be found by considering the vertical and horizontal components separately. To find the magnitude of the force, we can use Newton's second law which states that force is equal to mass multiplied by acceleration. For the vertical component, the force on the rider can be found by multiplying the mass of the rider by the downward component of acceleration. For the horizontal component, the force on the rider can be found by multiplying the mass of the rider by the horizontal component of acceleration.

Let's calculate the force on the rider for the given values. The vertical component of acceleration is 2.8 m/s² and the mass of the rider is 70 kg:

Vertical component force = mass × vertical component acceleration = 70 kg × 2.8 m/s² = 196 N

The force on the rider due to the vertical component of acceleration is 196 N.

Now let's calculate the force on the rider for the horizontal component of acceleration which is 6.0 m/s²:

Horizontal component force = mass × horizontal component acceleration = 70 kg × 6.0 m/s² = 420 N

The force on the rider due to the horizontal component of acceleration is 420 N.

To find the magnitude of the force on the rider by the sled, we can use the Pythagorean theorem because the vertical and horizontal components form a right triangle. The magnitude of the force can be found by taking the square root of the sum of the squares of the individual forces:

Magnitude of the force = sqrt((Vertical component force)^2 + (Horizontal component force)^2)

Magnitude of the force = sqrt((196 N)^2 + (420 N)^2)

Magnitude of the force = sqrt(38416 N² + 176400 N²)

Magnitude of the force = sqrt(214816 N²)

Magnitude of the force = 464 N

Therefore, the magnitude of the force on the rider by the sled is 464 N.

Answer 2

The magnitude of the force on the rider by the sled is 463.4 N.

Step-by-step explanation:

To find the magnitude of the force on the rider by the sled, we need to break down the sled's acceleration into its horizontal and vertical components.

Given that the sled's acceleration has a horizontal component of 6.0 m/s² and a downward component of 2.8 m/s², we can find the magnitude of the total acceleration using the Pythagorean theorem.

The total acceleration is √(6.0² + 2.8²) = √(36 + 7.84) = √(43.84) = 6.62 m/s².

Since the mass of the rider is 70 kg, we can find the magnitude of the force on the rider using Newton's second law, F = m * a.

Therefore, the magnitude of the force on the rider by the sled is 70 kg * 6.62 m/s² = 463.4 N.