a)An object on a frictionless surface forms an angle of 27° with the horizontal. The object is pushed by a horizontal external force such that it moves with a constant speed. If the mass of the object is 72.3 kg, calculate the magnitude of the external force.

b)What is the magnitude of the force exerted by the inclined surface on the object?

Weight = 72.3*9.8 = 708 N

component of weight normal to surface = 708*cos 27 = 631 N
component of weight down slope = 708 sin 27 = 322 N
Push force = F
component of push up slope = F cos 27
so
F cos 27 = 322 N
F = 361 N
component of F Normal to surface = 361 sin 27 = 164 N
total normal force on slope = 164+631 = 795 N

Soo what is a) supposed to be 164 and is b) 795?

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a) To calculate the magnitude of the external force, we can 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.

In this case, the object is moving with a constant speed, which means its acceleration is zero. Therefore, the net force acting on the object is also zero.

However, we need to consider the force due to gravity. The force of gravity can be calculated using the equation F = mg, where m is the mass of the object and g is the acceleration due to gravity (approximately 9.8 m/s²).

The force of gravity can be split into two components: one parallel to the inclined surface and one perpendicular to it. The component parallel to the inclined surface (F₁) can be calculated by multiplying the force of gravity (mg) by the sine of the angle formed with the horizontal surface. So,
F₁ = mg sinθ,

where θ is the angle formed by the object with the horizontal surface.

In this case, θ = 27° and m = 72.3 kg. Plugging these values into the equation, we get:
F₁ = 72.3 kg × 9.8 m/s² × sin(27°).

b) To find the magnitude of the force exerted by the inclined surface on the object, we can use the component of the force of gravity perpendicular to the inclined surface. This force is equal to the force of gravity multiplied by the cosine of the angle formed with the horizontal surface.

Using the same values from before (m = 72.3 kg and θ = 27°), the force exerted by the inclined surface on the object (F₂) can be calculated as:
F₂ = mg cosθ.

Substituting the values, we get:
F₂ = 72.3 kg × 9.8 m/s² × cos(27°).