(II) A person pushes a 14.0 -kg lawn mower at constant speed...

(II) A person pushes a 14.0 -kg lawn mower at constant speed with a force of $F=88.0 \mathrm{N}$ directed along the handle, which is at an angle of $45.0^{\circ}$ to the horizontal (Fig. $4-45 )$ . (a) Draw the free-body diagram showing all forces acting on the mower. Calculate (b) the horizontal friction force on the mower, then $(c)$ the normal force exerted vertically upward on the mower by the ground. (d) What force must the person exert on the lawn mower to accelerate it from rest to 1.5 $\mathrm{m} / \mathrm{s}$ in 2.5 seconds, assuming the same friction force?

(II) A person pushes a 14.0 -kg lawn mower at constant speed with a force of $F=88.0 \mathrm{N}$ directed along the handle, which is at an angle of $45.0^{\circ}$ to the horizontal (Fig. $4-45 )$ . (a) Draw the free-body diagram showing all forces acting on the mower. Calculate (b) the horizontal friction force on the mower, then $(c)$ the normal force exerted vertically upward on the mower by the ground. (d) What
force must the person exert on the lawn mower to accelerate it from rest to 1.5 $\mathrm{m} / \mathrm{s}$ in 2.5 seconds, assuming the same friction force?

Key Concepts

Force Decomposition

Force decomposition involves breaking down a force into its component parts along mutually perpendicular directions, such as horizontal and vertical components. This process is crucial when forces are applied at an angle, as it allows for the separate analysis of motion and effects in each direction, facilitating the application of Newton's laws of motion.

Free-Body Diagram

A free-body diagram is a graphical illustration used to visualize all the forces acting on an object. It typically represents the object as a point or simplified shape and draws vectors for forces such as gravity, normal force, applied forces, friction, and any other relevant interactions, making it an essential tool for analyzing mechanics problems.

Newton’s First Law

Newton’s First Law, also known as the law of inertia, states that an object will remain at rest or move with a constant velocity unless acted upon by a net external force. This concept is used to analyze situations where the object is moving at constant speed, indicating that the forces in different directions are balanced.

Friction

Friction is a resistive force that opposes the relative motion between surfaces in contact. It acts parallel to the contact surface and is determined by the nature of the surfaces and the normal force. In mechanics problems, friction must be considered when calculating the net force or analyzing situations where objects are moving or accelerating.

Normal Force

The normal force is the support force exerted by a surface perpendicular to the object in contact with it. It balances the component of the gravitational force acting on the object and any other vertical forces, and is particularly important when analyzing equilibrium or calculating frictional forces.

Newton’s Second Law

Newton’s Second Law of Motion states that the net force acting on an object is equal to the product of its mass and acceleration. This principle is fundamental for determining the acceleration of an object when a net force is applied, and it is also used to compute the additional force required to accelerate an object in the presence of other forces such as friction.

Transcript

00:01 In this question, learn over is a post person and here fly basically a force having magnitude 88 merton and the direction of 45 degree with the horizontal or vertical and mass of the this one is a 14 kg which is given so the first part of this question we need to we need to draw a big diagram so we're gonna do that for the first part where there a bit of diagram would look like something like this that obviously there will be a downward m g force due to the mass of this this one and that will be m g and obviously there will be normal due to the contact force and that will be in upper direction and obviously this force have f have two component one in vertical and one horizontal we don't do that that would be f upon two that means the cost of 45 really and one more force which will be opposing the motion that is friction force so this was the thing and that will be obviously acting in the backward direction backward direction so basically this was the force and now and we can say this is the 50 body diagram of this equation actually we can also you know obviously as i said earlier that we can also resolve a force but we're going to don't want to do that and in the next subsection we need to calculate the friction force acting on the on this blocks basically we know that f is equal to total force that will be the mass temps of acceleration over there and clearly in the acceleration over there that is zero actually or the direction acceleration in the direction of x or the acceleration over there is zero so we can say that we can say that that the sigma this total force over there that is is nothing but the one one component of the force that is in the forward direction and that would be f cost theta so we can say that f cost of theta and minus of friction force that would be zero because acceleration over there is zero we can say that the frequency force or the friction force acting on this one is equals to f of cost theta that means 88 times of course of 45 degree cost of 45 degrees cost of 45 degree that will basically comes out to be 62 .23 62 .23 newton now moving back to the next part of this question in which yeah so in this part and we need to again deal with the friction again so basically we're going to do that so see we have got to draw on the favorite diagram and we have calculated a friction force and in this question we need to calculate the the normal force actually so normal force that will be…

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